We develop the basic elements of a Cauchy theory on the complex Levi-Civita field, which constitutes the smallest algebraically closed nonArchimedean extension of the complex numbers. We introduce a concept of analyticity based on differentiation, and show that it leads to local expandability in power series. We show that analytic functions can be integrated over suitable piecewise smooths path...

The Levi-Civita (LC) solution is matched to a cylindrical shell of an anisotropic uid. The uid satis es the energy conditions when the mass parameter is in the range 0 1. The mass per unit length of the shell is given explicitly in terms of , which has a nite maximum. The relevance of the results to the non-existence of horizons in the LC solution and to gauge cosmic strings is pointed out. PAC...

Abstract We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated connection we can define a differential operator of first order. For any nonnull number k symmetric tensor field type (1,1) B on , (1,2) $$B^{(k)}_T$$ B</mml:m...

In this article, we consider a special case of Metric-Affine f(R)-gravity for f(R) = R, i.e. the General Relativity (MAGR). As companion to first article in series, perform (3+1) decomposition hypermomentum equation, obtained from minimization MAGR action S [g, {\omega}] with respect connection {\omega}. Moreover, show that tensor H could be constructed completely 10 hypersurfaces variables ari...

We apply a recent formalism of quantum geodesics to the well-known bicrossproduct model $\lambda$-Minkowski spacetime $[x^i,t]=\imath\lambda_p x^i$ with its flat metric as gravity effects, $\lambda_p$ Planck scale. As examples, geodesic flow plane wave gets an order frequency dependent correction classical velocity. A velocity $v$ Gaussian width $\sqrt{2\beta}$ initially centred at origin chang...

Because of the disconnectedness of a non-Archimedean ordered field in the topology induced by the order, it is possible to have non-constant functions with zero derivatives everywhere. In fact the solution space of the differential equation y′ = 0 is infinite dimensional. In this paper, we give sufficient conditions for a function on an open subset of the Levi-Civita field to have zero derivati...